SRC/slatrz.f(3)

NAME
SRC/slatrz.f

SYNOPSIS

  Functions/Subroutines
subroutine slatrz (m, n, l, a, lda, tau, work)
SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

Function/Subroutine Documentation

  subroutine slatrz (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work)

SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

Purpose:

    !>
    !> SLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
    !> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z, by means
    !> of orthogonal transformations.  Z is an (M+L)-by-(M+L) orthogonal
    !> matrix and, R and A1 are M-by-M upper triangular matrices.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    L

    !>          L is INTEGER
    !>          The number of columns of the matrix A containing the
    !>          meaningful part of the Householder vectors. N-M >= L >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the leading M-by-N upper trapezoidal part of the
    !>          array A must contain the matrix to be factorized.
    !>          On exit, the leading M-by-M upper triangular part of A
    !>          contains the upper triangular matrix R, and elements N-L+1 to
    !>          N of the first M rows of A, with the array TAU, represent the
    !>          orthogonal matrix Z as a product of M elementary reflectors.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    TAU

    !>          TAU is REAL array, dimension (M)
    !>          The scalar factors of the elementary reflectors.
    !>

    WORK

    !>          WORK is REAL array, dimension (M)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>
    !>  The factorization is obtained by Householder's method.  The kth
    !>  transformation matrix, Z( k ), which is used to introduce zeros into
    !>  the ( m - k + 1 )th row of A, is given in the form
    !>
    !>     Z( k ) = ( I     0   ),
    !>              ( 0  T( k ) )
    !>
    !>  where
    !>
    !>     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
    !>                                                 (   0    )
    !>                                                 ( z( k ) )
    !>
    !>  tau is a scalar and z( k ) is an l element vector. tau and z( k )
    !>  are chosen to annihilate the elements of the kth row of A2.
    !>
    !>  The scalar tau is returned in the kth element of TAU and the vector
    !>  u( k ) in the kth row of A2, such that the elements of z( k ) are
    !>  in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
    !>  the upper triangular part of A1.
    !>
    !>  Z is given by
    !>
    !>     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
    !>

Definition at line 139 of file slatrz.f.

Author

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